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The Higgs-boson production in association with a W-boson pair at $e^+e^-$linear colliders is one of the important processes in probing the couplingbetween Higgs-boson and vector gauge bosons and discovering the signature ofnew physics. We describe the impact of the complete electroweak(EW) radiativecorrections of ${\cal O}(\alpha_{ew})$ to this process in the standardmodel(SM) at the International Linear Collider(ILC), and investigate thedependence of the lowest-order(LO) and EW next-to-leading order(NLO) correctedcross sections on colliding energy $\sqrt{s}$ and Higg-boson mass. The LO andNLO EW corrected distributions of the invariant mass of W-boson pair and thetransverse momenta of final $W$- and Higgs-boson are presented. Our numericalresults show that the relative EW radiative correction($\delta_{ew}$) variesfrom -19.4% to 0.2% when $m_H=120 GeV$ and $\sqrt{s}$ goes up from $300 GeV$ to$1.2 TeV$.

Precise predictions for the Higgs production in association with a W-boson pair at ILC